Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)
double f(double x, double y, double z) {
        double r239265 = x;
        double r239266 = y;
        double r239267 = r239265 * r239266;
        double r239268 = 1.0;
        double r239269 = r239268 - r239265;
        double r239270 = z;
        double r239271 = r239269 * r239270;
        double r239272 = r239267 + r239271;
        return r239272;
}
↓
double f(double x, double y, double z) {
        double r239273 = x;
        double r239274 = y;
        double r239275 = 1.0;
        double r239276 = r239275 - r239273;
        double r239277 = z;
        double r239278 = r239276 * r239277;
        double r239279 = fma(r239273, r239274, r239278);
        return r239279;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)}\]
  3. Using strategy rm

  4. Applied pow10.0

    \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\right)}^{1}}\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1 x) z)))